1. Experiment: Picking a card from a fair deck.

Sample space:

{AH, 2H, 3H, 4H, 5H, 6H, 7H, 8H, 9H, 10H, JH,QH, KH

AD, 2D, 3D, 4D, 5D, 6D, 7D, 8D, 9D, 10D, JD,QD, KD

AC, 2C, 3C, 4C, 5C, 6C, 7C, 8C, 9C, 10C, JC,QC, KC

AS, 2S, 3S, 4S, 5S, 6S, 7S, 8S, 9S, 10S, JS,QS, KS}

a) The face cards are King (K), Queen (Q), and Jack (J). What is the probability of picking a King given that the card is a face card?

b) Are the events "pick a King" and "pick a face card"independent events? Justify your answer with a probability calculation.